When you have completed this exercise, you will know how to calculate thepower contained in the wind, and how wind power varies with wind speed. Youwill learn that only a fraction of the power in the wind intercepted by the blades ofa wind turbine is transferred to the rotor, and then converted into electrical power.You will be familiar with the typical torque-versus-speed curve and mechanicalpower-versus-speed curve at the rotor of a wind turbine. You will be familiar withthe corresponding current-versus-voltage curve and electrical power-versusspeed curve at the wind turbine generator output. You will know how all of thesecurves are affected by wind speed. You will also know what the optimum rotorspeed and torque are, and how they are related to the maximum power point ofthe wind turbine.

DISCUSSIONOUTLINE

The Discussion of this exercise covers the following points:

DISCUSSION

Air densityKinetic energy in the windCalculating wind powerRelationship between wind power and wind speedRelationship between torque, rotation speed, and rotational mechanicalpowerConversion of wind power into rotational mechanical power and electricalpowerTypical torque-versus-speed curve at the wind turbine rotorTorque-versus-speed and mechanical power-versus-speed curves at thewind turbine rotor for different wind speedsCurrent-versus-voltage and electrical power-versus-speed curves at thewind turbine generator output for different wind speedsWind turbine generator efficiency

AirdensityThe air density, symbolized by the Greek letter (rho), is an importantparameter to know in wind power applications. Air density is the mass of air perunit volume:

is the air density, in kilograms per cubic meter (kg/m3)

Exercise 3 Power Versus Wind Speed Discussion

The air density varies with atmospheric pressure, temperature, humidity, andaltitude:

In S.I. units, is equal to 1.225 kg/m3 under standard sea level conditions,which are: a temperature of 15.5C, an atmospheric pressureof 101.325 kPa, and a relative humidity of 36%.

In U.S. customary units, is equal to 0.076 lbm/ft3 under standard (sea

level) conditions, which are: a temperature of 60F, an atmospheric pressureof 14.7 psia or 0 psig, and a relative humidity of 36%.

KineticenergyinthewindAny object or fluid in motion has kinetic energy. For example, wind, which is amass of air in motion, has kinetic energy. The faster the speed of the wind, thehigher the kinetic energy of the wind.The kinetic energy in a mass of air in motion can be calculated by using thefamiliar equation:

where

(4)

is the kinetic energy, in joules (J) [feet-pound force (ftlbf)].

is the mass of air, in kilograms (kg) [pounds mass (lbm)]. is the velocity of the mass of air, in meters per second (m/s)[feet per second (ft/s)].2is a constant. When working in U.S. customary units, thisconstant must be multiplied by the gravitational constant, (32.174 lbmft/lbfs2).The gravitational constant, must be used to change frompounds mass (lbm) to pounds force (lbf). The equation for calculating kineticenergy is, therefore:

Where is equal to 32.174 lbmft/lbfs .

Note that the term wind speed is also used to designate the wind velocity, .

CalculatingwindpowerFigure 23 shows wind of constant speed passing through a cross-sectionalarea, . This area could be, for example, the area swept by the blades of a windturbine.

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Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Discussion

Cross-sectional area,

Wind speed,

Wind

Figure 23. Wind flowing through a cross-sectional area.

In S.I. units, the power in the wind passing through the cross-sectional area is:

where

(5)

is the power in the wind, in watts (W, or kgm2/s3).

is the air density, in kilograms per cubic meter (kg/m3).is the cross-sectional area, in square meters (m2).is the wind speed, in meters per second (m/s).

In U.S. customary units, the power in the wind passing through the crosssectional area is:

where

(6)

is the power in the wind, in feet-pound force per second (ftlbf/s).

is the air density, in pounds mass per cubic foot (lbm/ft3).is the cross-sectional area, in square feet (ft2).is the wind speed, in feet per second (ft/s).is the gravitational constant, equal to 32 174 lbmft/lbfs2.

The following observations can be made from the above equations:

Any change in the temperature of the air, atmospheric pressure, or relative

humidity causes the air density to change, causing the wind power tochange in the exact same way (for given wind speed and cross-sectionalarea). For instance, when the air density increases by 5%, the windpower also increases by 5%.

When the cross-sectional area, , swept by the blades of a wind turbine rotoris increased, the wind power intercepted by the blades increases in directproportion.

When the wind speed, increases, the wind power also increases.

A Introduction to Wind Power

39

Exercise 3 Power Versus Wind Speed Discussion

RelationshipbetweenwindpowerandwindspeedAs mentioned above, the wind power increases when the wind speed increases.More precisely, the wind power varies with the cube (the third power) of thewind speed, , as Figure 24 shows.

Wind speed (mph)

Power (W/m )

Wind speed (km/h)

Wind speed (m/s)

Figure 24. The wind power varies with the cube (the third power) of the wind speed.

Relationshipbetweentorque,rotationspeed,androtationalmechanicalpowerWhen a force is applied to an object mounted on a rotation axis (such as thebladed rotor of a wind turbine, the object starts to rotate at a certain speed, asshown in Figure 25. The rotation speed, , is expressed in revolutions per

40

Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Discussion

minute (r/min). One revolution is equal to 360, or 2 (6.28) radians (rad), oneradian (1 rad) being equal to 57.3.

Figure 25. Torque, rotation speed, and rotational mechanical power.

The rotational mechanical power produced at the rotating axis of the object, ,is the product of the torque developed at the rotating axis and the rotationspeed, , divided by a constant.The equation below allows the rotational mechanical power to be calculatedwhen S.I. units are used:

where

(7)

is the rotational mechanical power, in watts (W).

is the torque, in newton meters (Nm).is the rotation speed, in revolutions per minute (r/min).is a constant.

When U.S. customary units are used, the equation is the same, but the constantis different:

where

A Introduction to Wind Power

(8)

is the rotational mechanical power, in watts (W).

is the torque, in pound-force inches (lbfin).is the rotation speed, in revolutions per minute (r/min).is a constant.

Exercise 3 Power Versus Wind Speed Discussion

ConversionofwindpowerintorotationalmechanicalpowerandelectricalpowerWhen wind hits the blades of a wind turbine rotor, the pressure of the air actingon the surface of the blades creates a force, which applies a torque onto the rotorof the turbine, as Figure 26 shows.When the wind is strong enough to produce a torque higher than the force(torque) opposing rotation, the wind turbine rotor starts to rotate at a certainspeed. In this condition,

the blades of the wind turbine convert a portion of the power contained in thewind they intercept (linear mechanical power) into rotational mechanicalpower that makes the wind turbine rotor turn.

the rotational mechanical power produced at the wind turbine rotor drives anelectric generator. The electric generator converts the rotational mechanicalpower into electrical power.Three-blade windturbine rotor

Wind turbinegenerator

Figure 26. A fraction of the power in the wind intercepted by the blades of the turbine isconverted into rotational mechanical power to drive the electric generator of the turbine.

Wind,rotor,androtorefficiencycoefficient, As already mentioned, the power contained in the wind passing through the areaswept by the blades of a wind turbine rotor is:

where

42

(9)

is the power in the wind.

is the air density.is the cross-sectional area swept by the wind turbine rotor.is the wind speed.

Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Discussion

Not all the power in the wind passing through the swept area is transferred to thewind turbine rotor. Only a fraction of the available wind power is extracted by theblades and transferred to the rotor. This fraction indicates the efficiency of thewind turbine rotor in converting linear mechanical power into rotationalmechanical power.The fraction of wind power extracted by the blades and transferred to the rotor iscalled the rotor coefficient efficiency . The rotor efficiency coefficient dependson the design (shape) of the rotor blades. The rotor efficiency coefficient issometimes expressed as a percentage (rotor efficiency coefficient multipliedby 100%).The rotor efficiency coefficient is generally between 0.4 and 0.5 for most bladedesigns. The rotor efficiency coefficient must be taken into account todetermine the fraction of wind power that is transferred to the wind turbinerotor. The formula used to calculate the mechanical power at the wind turbinerotor, , is, therefore:

(10)

The rotor efficiency coefficient of a wind turbine is virtually constant over thenormal wind speed range of the turbine. Therefore, the mechanical power at thewind turbine rotor varies in the same way as wind power, that is, with the cube(the third power) of the wind speed.

TypicaltorqueversusspeedcurveatthewindturbinerotorFigure 27 shows a typical torque-versus-speed curve at the rotor of a windturbine obtained for a given wind speed.As the rotor speed increases, the torque produced at the rotor increases until apoint is reached, beyond which the torque gradually decreases to zero.Consequently, the mechanical power produced at the rotor also increases up to acertain maximum value, and then gradually decreases to zero, as Figure 27shows. The point at which the mechanical power is maximum is referred to asthe maximum power point (MPP). The rotor speed and torque at the MPP arecommonly referred to as the optimum speed and optimum torque,respectively.A wind turbine must be operated as close as possible to the optimum speed tomaximize the mechanical power developed at the rotor and thus obtain themaximum amount of electrical power. This is performed by setting the rotortorque to the optimum value, through adjustment of the current drawn by theelectrical load at the wind turbine generator output.

TorqueversusspeedandmechanicalpowerversusspeedcurvesatthewindturbinerotorfordifferentwindspeedsFigure 28 shows a set of typical curves at the rotor of a wind turbine, for differentwind speeds: the torque-versus-speed curves (section a) and the mechanicalpower-versus-speed curves (section b).On each torque-versus-speed curve in Figure 28a, a diamond-shaped markerindicates the optimum rotor torque and speed at which the maximum amount ofmechanical power is produced at the wind turbine rotor. The maximum powerpoint (MPP) is also indicated by a diamond-shaped marker on each of thecorresponding mechanical power curves in Figure 28b.Note that the rotor speed at which the maximum amount of mechanical power isproduced at the rotor of a wind turbine varies with the wind speed. Therefore, tooperate the wind turbine at the maximum power point (MPP) and maximize theenergy produced at any wind speed, the rotor speed must be continuouslymonitored and kept at the optimum value, through adjustment of the rotor torquewhen necessary. This is generally performed automatically by a controller in thewind turbine, as you will see in the next exercise.

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Exercise 3 Power Versus Wind Speed Discussion

Wind speed

Rotor torque (Nm)

Point of optimum rotor torque and

speed at a wind speed of 12 m/s

Rotor speed (r/min)

(a) Torque-versus-speed curves

Mechanical power at rotor (W)

Wind speed

Maximum power point (MPP)

at a wind speed of 12 m/s

Rotor speed (r/min)

(b) Mechanical power-versus-speed curves

Figure 28. Family of typical curves at the bladed rotor of a wind turbine, for different windspeeds.

The following conclusions can be drawn from examination of the family of curvesin Figure 28.

Consequently, higher amounts of mechanical power are produced at the

rotor when the wind speed increases, as Figure 28b shows.

A Introduction to Wind Power

45

Exercise 3 Power Versus Wind Speed Discussion

When the maximum power points on the various mechanical power curves inFigure 28b are connected together, they form a curve which increasesexponentially (see dashed line in Figure 28b. In fact, the mechanical power at theMPPs increases by eight whenever the wind speed doubles. This occursbecause the power in the wind varies with the cube (the third power) of the windspeed.

CurrentversusvoltageandelectricalpowerversusspeedcurvesatthewindturbinegeneratoroutputfordifferentwindspeedsFigure 29 shows a set of typical curves related to the output of a wind turbinegenerator, for different wind speeds: the current-versus-voltage curves of thegenerator output (section a) and the corresponding electrical power-versusspeed curves (section b).The following conclusions can be drawn by comparing the family of curves inFigure 29 with the family of curves in Figure 28:

The voltage and current at the output of the wind turbine generator areproportional to the speed and torque at the wind turbine rotor, respectively.Consequently the current-versus-voltage curves of the wind turbinegenerator (Figure 29a) are similar to the torque-versus-speed curves at thewind turbine rotor (shown in Figure 28a).

Also, the electrical power-versus-speed curves of the wind turbine generator

(Figure 29b) are similar to the mechanical power-versus-speed curves at thewind turbine rotor (shown in Figure 28b).

Through proper control of the electrical load applied to the wind-turbine generatoroutput, the rotor speed and torque can be adjusted in order to keep the generatoroperating at the maximum power point (MPP) at any wind speed.

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Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Discussion

Wind speed

Generator current (A)

Point of optimum voltage

and current at a windspeed of 12 m/s

Generator voltage (V)

(a) Current-versus-voltage curves

Electrical power at generator output (W)

Wind speed

Maximum power point

(MPP) at a wind speedof 12 m/s

Rotor speed (r/min)

(b) Electrical power-versus-speed curves

Figure 29. Family of typical curves related to the output of a wind turbine generator, fordifferent wind speeds.

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47

Exercise 3 Power Versus Wind Speed Discussion

WindturbinegeneratorefficiencyWhenever a current flows through a conductor, power is lost as heat through theresistance of the conductor. The higher the current flowing through theconductor, the greater the power lost through the conductor. In fact, the amountof power lost increases with the square of the current through the conductor. Theamount of power lost is also determined by the resistance of the conductor. Thisresistance is directly proportional to the length of the conductor and inverselyproportional to the cross-sectional area of the conductor.With a wind turbine generator (as well as any other generator), not all themechanical power applied to the rotor shaft is converted into electrical power,due to power losses in the stator windings. These power losses are usuallycalled I2R losses. They decrease the efficiency of a wind turbine in convertingmechanical power into electrical power. As a result, the actual curves of currentversus voltage and electrical power versus speed of a wind turbine generatordiffer significantly from the ideal curves you have studied so far, both in shapeand amplitude, particularly at high wind speeds.As an example, Figure 30 shows the ideal and actual curves related to a windturbine generator at a wind speed of 10 m/s.

48

Figure 30a shows that the actual current-versus-voltage curve is shifted

toward the left with respect to the ideal curve. This indicates that the actualgenerator voltage is lower than expected. For instance, on the ideal curve,the point of optimum voltage and current occurs at a generator voltage of68 V and a generator current of 3.3 A. On the actual curve, the point ofoptimum voltage and current occurs at a lower generator voltage of 52 V anda current of 3.4 A. This occurs because the I2R losses through the generatorwindings result in a certain voltage drop across these windings, causing thegenerator voltage to be lower than expected.

Figure 30b shows that the actual electrical power produced by the generatoris lower than the ideal power value over most of the rotor speed range. Onthe ideal curve, the maximum electrical power is 224 W, and it is reachedwhen the rotor speed is 987 r/min. On the actual curve, the maximumelectrical power is 177 W, and it is reached when the rotor speed is1013 r/min. Therefore, the actual electrical power produced by the generatoris lower than the ideal value by 47 W, which corresponds to a powerconversion efficiency of about 79% (177 W 224 W).

A Introduction to Wind Power

Exercise 3 Power Versus Wind Speed Procedure Outline

The Procedure is divided into the following sections:

Equipment setup and friction compensation calibration

Plotting the characteristic curves of the wind turbine for different windspeeds

PROCEDUREHigh voltages are present in this laboratory exercise. Do not make ormodify any banana jack connections with the power on unless otherwisespecified.

EquipmentsetupandfrictioncompensationcalibrationIn this section, you will set up the equipment. You will use a prime mover toemulate the wind blowing onto the blades of a wind turbine rotor driving agenerator.1. Refer to the Equipment Utilization Chart in Appendix A to obtain the list ofequipment required to perform the exercise.Install the equipment required in the Workstation.Mechanically couple the Wind Turbine Generator/Controller module to theFour-Quadrant Dynamometer/Power Supply.

Before coupling rotating machines, make absolutely sure that power is

turned off to prevent any machine from starting inadvertently.

2. Set the main power switch of the Four-Quadrant Dynamometer/Power

Supply to the O (off) position, then connect the Power Input to an ac poweroutlet.Set the Operating Mode switch of the Four-Quadrant Dynamometer/PowerSupply to Dynamometer. This setting allows the Four-QuadrantDynamometer/Power Supply to operate as a prime mover, a brake, or both,depending on the selected function.Connect the Four-Quadrant Dynamometer/Power Supply to a USB port ofthe host computer.Turn the Four-Quadrant Dynamometer/Power Supply on by setting the mainpower switch to I (on).

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Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Procedure

3. Turn the host computer on, then start the LVDAC-EMS software.In the LVDAC-EMS Start-Up window, make sure that the Four-QuadrantDynamometer/Power Supply is detected. Make sure that the TurbineEmulator function is available for the Four-Quadrant Dynamometer/PowerSupply. Select the network voltage and frequency that correspond to thevoltage and frequency of your local ac power network, then click theOK button to close the LVDAC-EMS Start-Up window.4. In LVDAC-EMS, open the Four-Quadrant Dynamometer/Power Supplywindow. In the Tools menu of this window, select Friction CompensationCalibration, which will bring up the Friction Compensation Calibration dialogbox. Click OK in this box to start the calibration process. Observe that theprime mover starts to rotate at high speed, thereby driving the shaft of thewind turbine generator. The prime mover speed is then automaticallydecreased by steps to perform the calibration process. Once the calibrationprocess is completed (which takes about two minutes), the prime moverstops rotating, then the Friction Compensation Calibration dialog boxindicates that the calibration process is finished. Click OK in the FrictionCompensation Calibration dialog box to close this box. Restart the FourQuadrant Dynamometer/Power Supply to apply the changes (i.e., the newlycalibrated friction compensation curve) by setting the main power switch ofthis module to O (off), and then I (on).5. Set up the circuit shown in Figure 31. In this setup, the prime mover drivesthe wind turbine generator, thereby producing an ac voltage across thegenerator windings. A diode rectifier in the Wind TurbineGenerator/Controller converts this ac voltage into dc voltage to supplyelectrical dc power to a variable resistive load, (5 to infinite ).The resistive load is implemented with the Resistive Load module forresistance values between 57 and 1200 , or with the Load Resistors onthe Wind turbine Generator/Controller for resistance values between 5 and45 .Connect the Diode Rectifier output of the Wind Turbine Generator/Controllerto the Resistive Load module. Connect the three resistor sections on thismodule in parallel. Then, set the initial load resistance value to infinite ( )by placing the levers of all the toggle switches to the O (off) position.Set a multimeter to measure dc current and connect it in series with theDiode Rectifier output, as Figure 31 shows. DC currents up to 5 A can beexpected at high wind speeds. Therefore, make sure to set your multimeteraccordingly.Set a multimeter to measure dc voltage and connect it across the load, asFigure 31 shows.

A Introduction to Wind Power

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Exercise 3 Power Versus Wind Speed Procedure

Wind Turbine Generator/Controller (8216)

Primemover

Rotor

(5 to )

GeneratorwindingsDiode rectifier

Figure 31. Equipment setup.

6. In the Four-Quadrant Dynamometer/Power Supply window of LVDAC-EMS,

make the following settings:

Set the Function parameter to Small Wind Turbine Emulator. This settingmakes the Four-Quadrant Dynamometer/Power Supply operate as aprime mover emulating wind blowing onto the blades mounted at the endof the wind turbine rotor. Therefore, the prime movers torque-versusspeed characteristic is the same as the torque-versus-speedcharacteristic that would be obtained at the wind turbine rotor for differentwind speeds. In other words, the wind turbine generator operates as if itwere driven by wind blowing onto the rotor blades, but without the needof wind or blades.

Make sure that the Wind Control parameter is set to Slider.

Make sure that the Wind Turbine Type parameter is set to 200 W, 1.15 m3 blade rotor, fixed pitch.

Leave the other parameters set as they are.

a

52

The Pulley Ratio parameter is grayed out since it is automatically set to therequired value (24:32).

Ensure the continuous refresh mode of the meters is enabled. The

continuous refresh mode of the meters is enabled by clicking the.Continuous Refresh button

Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Procedure

PlottingthecharacteristiccurvesofthewindturbinefordifferentwindspeedsIn this section, you will plot the characteristic curves of the wind turbine. Thesecurves are the torque-speed and mechanical power-speed curves at the windturbine rotor, as well as the corresponding current-voltage and electrical powerspeed curves of the wind turbine generator, for different wind speeds. You willcompare the shapes of these curves, and describe how they vary with windspeed. You will determine the maximum power point for each wind speed.Measurementsatawindspeedof4m/s(14.4km/hor9.0mph)7. Make the wind turbine generator operate as if the wind is blowing at 4 m/sonto the rotor blades by making the following settings in the Four-QuadrantDynamometer/Power Supply window:

Set the Wind Speed parameter to 4 m/s (14.4 km/h or 9 mph).

Start the prime mover (small wind turbine emulator) by setting the Statusparameter to Started or by clicking on the Start/Stop button.

Observe that the prime mover starts to rotate, thereby driving the rotor of thewind turbine generator as if wind were blowing at 4 m/s onto the rotor blades.Since the resistance of the load is maximum ( ), the generator rotationspeed is also maximum.In Table 3, record the rotation speed, torque (absolute value), andmechanical power (absolute value) at the wind turbine rotor. Theseparameters are indicated by the Speed, Torque, and Power meters,respectively, in the Four-Quadrant Dynamometer/Power Supply window.Also, measure and record the dc voltage and dc current supplied to the loadby the wind turbine generator.

A Introduction to Wind Power

53

Exercise 3 Power Versus Wind Speed Procedure

Table 3. Measuring the parameters of the wind turbine at a wind speed of 4 m/s (14.4 km/hor 9.0 mph).

(eight to ten points) spread all along the typical torque-versus-speed curve(see Figure 27). To do this, gradually decrease the load resistance and, foreach resistance setting, record the rotation speed, torque (absolute value),and mechanical power (absolute value) at the wind turbine rotor in Table 3.Also, measure and record the dc voltage and dc current supplied to the loadby the wind turbine generator.The following resistance settings are suggested: 400 , 150 , 75 , 45 ,30 , 15 , 7.5 , and 5 . For the minimum generator rotation speed, setthe load resistance to 0 by short-circuiting the output of the Diode Rectifieron the Wind Turbine Generator/Controller via the dc ammeter.

When the Load Resistors of the Wind Turbine/Generator Controller are

used, stop the prime mover before modifying any connection betweenthese resistors to prevent the risk of an electrical shock.

When using the 15- Load Resistor alone, take your measurements within oneminute and then stop the prime mover to prevent this resistor from overheating.

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Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Procedure

Appendix C of this manual lists the switch settings to be performed on the

Resistive Load module in order to insert various resistance values into thecircuit. The resistance provided by the Resistive Load module cannot bedecreased below 57 . To further decrease the load resistance, stop the primemover (small wind turbine emulator), then disconnect the Diode Rectifieroutput of the Wind Turbine Generator/Controller from the Resistive Loadmodule. On the Wind Turbine Generator/Controller, connect the DiodeRectifier output to the Load Resistors and connect these resistors in order toset the load resistance to different values. The possible resistor arrangements(series, parallel, series-parallel) provide resistance values between 5 and45 . Be sure to include the ammeter and the voltmeter in the circuit in orderto measure the dc voltage and dc current supplied to the load, as shown inFigure 31. For each load resistance setting, start the prime mover and recordthe rotation speed, torque, and mechanical power at the wind turbine rotor inTable 3. Also, record the dc voltage and dc current supplied to the load by thewind turbine generator. Stop the prime mover before modifying any connectionbetween these Load Resistors.

9. Stop the prime mover, remove the short-circuit at the Diode Rectifier output,and disconnect the Load Resistors.10. Based on the dc voltages and dc currents recorded in Table 3, calculate theelectrical power supplied to the load for each rotation speed and record yourresults in the table.Measurements at a wind speed of 7 m/s (25.2 km/h or 15.7 mph)11. Ensure the prime mover is stopped. On the Wind TurbineGenerator/Controller, connect the Diode Rectifier output of the Wind TurbineGenerator/Controller to the Resistive Load module. Then, set the initial loadresistance value to infinite ( ) by placing the levers of all the toggleswitches to the O (off) position.Connect the multimeter set to measure dc current in series with the DiodeRectifier output, as Figure 31 shows. Connect the multimeter set to measuredc voltage across the load, as Figure 31 shows.12. Make the wind turbine generator operate as if wind were blowing at 7 m/sonto the rotor blades by making the following settings in the Four-QuadrantDynamometer/Power Supply window:

Set the Wind Speed parameter to 7 m/s (25.2 km/h or 15.7 mph).

Start the prime mover by setting the Status parameter to Started or by

clicking on the Start/Stop button. Since the resistance of the load ismaximum ( ), the generator rotation speed is also maximum.

In Table 4, record the rotation speed, torque (absolute value), and

mechanical power (absolute value) at the wind turbine rotor. Theseparameters are indicated by the Speed, Torque, and Power meters,respectively, in the Four-Quadrant Dynamometer/Power Supply window.Also, measure and record the dc voltage and dc current supplied to the loadby the wind turbine generator.

A Introduction to Wind Power

55

Exercise 3 Power Versus Wind Speed Procedure

Table 4. Measuring the parameters of the wind turbine at a wind speed of 7 m/s (25.2 km/hor 15.7 mph).

rotation speed by decreasing the load resistance in order to obtain severalpoints spread all along the typical torque-versus-speed curve. For eachresistance setting, record the rotation speed, torque (absolute value), andmechanical power (absolute value) at the wind turbine rotor in Table 4. Also,measure and record the dc voltage and dc current supplied to the load by thewind turbine generator.The following resistance settings are suggested: 240 , 120 , 71 , 45 ,30 , 15 , 7.5 , and 5 . For the minimum generator rotation speed, setthe load resistance to 0 by short-circuiting the output of the Diode Rectifieron the Wind Turbine Generator/Controller via the dc ammeter.

When the Load Resistors of the Wind Turbine/Generator Controller are used,stop the prime mover before modifying any connection between theseresistors to prevent the risk of an electrical shock.

When using the 15- Load Resistor alone, take your measurements within oneminute and then stop the prime mover to prevent this resistor from overheating.

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Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Procedure

14. Stop the prime mover, remove the short-circuit at the Diode Rectifier output,and disconnect the Load Resistors.15. Based on the dc voltages and dc currents recorded in Table 4, calculate theelectrical power supplied to the load for each rotation speed and record yourresults in the table.Measurementsatawindspeedof10m/s(36km/hor22.4mph)16. Ensure the prime mover is stopped. On the Wind TurbineGenerator/Controller, connect the Diode Rectifier output of the Wind TurbineGenerator/Controller to the Resistive Load module. Then, set the initial loadresistance value to infinite ( ) by placing the levers of all the toggleswitches to the O (off) position.Connect the multimeter set to measure dc current in series with the DiodeRectifier output, as Figure 31 shows. Connect the multimeter set to measuredc voltage across the load, as Figure 31 shows.17. Make the wind turbine generator operate as if wind were blowing at 10 m/sonto the rotor blades by making the following settings in the Four-QuadrantDynamometer/Power Supply window:

Set the Wind Speed parameter to 10 m/s (36 km/h or 22.4 mph).

Start the prime mover by setting the Status parameter to Started or by

clicking on the Start/Stop button. Since the resistance of the load ismaximum ( ), the generator rotation speed is also maximum.

In Table 5, record the rotation speed, torque (absolute value), and

mechanical power (absolute value) at the wind turbine rotor. Theseparameters are indicated by the Speed, Torque, and Power meters,respectively, in the Four-Quadrant Dynamometer/Power Supply window.Also, measure and record the dc voltage and dc current supplied to the loadby the wind turbine generator.

A Introduction to Wind Power

57

Exercise 3 Power Versus Wind Speed Procedure

Table 5. Measuring the parameters of the wind turbine at a wind speed of 10 m/s (36 km/hor 22.4 mph).

rotation speed by decreasing the load resistance so as to obtain severalpoints spread all along the typical torque-versus-speed curve. For eachresistance setting, record the rotation speed, torque (absolute value), andmechanical power (absolute value) at the wind turbine rotor in Table 5. Also,measure and record the dc voltage and dc current supplied to the load by thewind turbine generator.The following resistance settings are suggested: 200 , 86 , 45 , 30 ,15 , 7.5 , and 5 . For the minimum generator rotation speed, set the loadresistance to 0 by short-circuiting the output of the Diode Rectifier on theWind Turbine Generator/Controller via the dc ammeter.

When the Load Resistors of the Wind Turbine/Generator Controller are

used, stop the prime mover before modifying any connection betweenthese resistors to prevent the risk of an electrical shock.

When using the 15- Load Resistor alone, take your measurements within oneminute and then stop the prime mover to prevent this resistor from overheating.

19. Stop the prime mover.

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Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Procedure

20. Based on the dc voltages and dc currents recorded in Table 5, calculate theelectrical power supplied to the load for each rotation speed and record yourresults in the table.21. From the results recorded in Table 3, Table 4, and Table 5, plot in one graphthe torque-versus-speed curves at the wind turbine rotor for wind speeds of4, 7, and 10 m/s.Then, plot in one graph the dc current-versus-dc voltage curves of the windturbine generator for wind speeds of 4, 7, and 10 m/s.Compare the plotted curves. Do the dc current-versus-dc voltage curveshave a shape similar to that of the torque-versus-speed?

Yes

No

22. From the results recorded in Table 3, Table 4, and Table 5, plot in one graphthe mechanical power-versus-speed curves at the wind turbine rotor for windspeeds of 4, 7, and 10 m/s.Then, plot in one graph the electrical power-versus-speed curves of the windturbine generator for wind speeds of 4, 7, and 10 m/s.Compare the plotted curves. Do the electrical power-versus-speed curveshave a shape similar to that of the mechanical power-versus-speed curves?

Yes

No

23. On the mechanical power-versus-speed and electrical power-versus speed

curves, notice that, for each wind speed, the mechanical power and electricalpower are both maximum at a particular rotation speed. In Table 6, recordthe maximum mechanical power and maximum electrical power for eachwind speed. Also, record the rotation speed and torque at the wind turbinerotor when the mechanical power and electrical power are maximum. Thesespeed and torque values correspond to the optimum speed and optimumtorque.Notice that for each wind speed in Table 6, the maximum electrical power islower than the maximum mechanical power, especially at a wind speed of10 m/s. Briefly explain why.

4 m/s (14.4 km/h

or 9.0 mph)7 m/s (25.2 km/hor 15.7 mph)10 m/s (36 km/hor 22.4 mph)

24. Calculate the wind turbine generator efficiency at the maximum power pointsfor each wind speed. Record your results in Table 6. Based on your results,how does the generator efficiency vary when the wind speed increases?Why?

25. Based on the results recorded in Table 6, plot a rough curve of the maximummechanical power as a function of wind speed. Also, plot on the same grapha rough curve of the maximum electrical power as a function of wind speed.Does the curve of maximum mechanical power as a function of wind speedconfirm that the mechanical power developed at the wind turbine rotor isproportional to the cube (the third power) of the wind speed?

Yes

No

Does the curve of maximum electrical power as a function of wind speed

show that the maximum electrical power at the wind turbine generator isproportional to the cube (the third power) of the wind speed? If not, explainwhy.

26. In the Tools menu of the Four-Quadrant Dynamometer/Power Supply

window, select Reset to Default Friction Compensation. This will bring up theReset Friction Compensation dialog box. Click Yes in this window to resetthe friction compensation to the factory default compensation.27. Close LVDAC-EMS, then turn off all equipment. Remove all leads andcables.

60

Introduction to Wind Power A

Exercise 3 Power Versus Wind Speed Conclusion

CONCLUSION

In this exercise, you learned that the power contained in the wind varies with thecube (the third power) of the wind speed. You learned that only a fraction of thepower passing through the area swept by the blades of a wind turbine rotor isextracted by the blades and transferred to the rotor. This fraction is proportionalto the rotor efficiency coefficient, noted . You became familiar with the torqueversus-speed curve at the rotor of a wind turbine. You saw that, for any windspeed, there is a point of optimum speed and optimum torque, at which themechanical power produced at the rotor is maximum. At that point, called themaximum power point or MPP, the electrical power produced by the wind turbinegenerator is also maximum. You learned that the maximum mechanical powerpoint varies with the cube (the third power) of the wind speed. Therefore, tooperate a wind turbine at the maximum power point and maximize the energyproduced at any wind speed, the rotor speed must be continuously monitoredand kept at the optimum value, through adjustment of the rotor torque.

REVIEWQUESTIONS

1. Calculate the amount of power in the wind passing through the area swept bya wind turbine rotor, if the swept area is 10 m2 (107.6 ft2), the windspeed is 4.5 m/s (14.8 ft/s), and the air density is 1.225 kg/m3(0.076 lbm/ft3).

2. By how much does the power in the wind passing through a given crosssectional area increase, when the wind speed doubles? When the windspeed triples? Explain by describing how the power in the wind varies withwind speed.

3. What is meant by the rotor efficiency coefficient? What does it indicate?

Calculate the amount of mechanical power transferred at the rotor of a windturbine, , when the wind power swept by the rotor blades, , is 500 Wand the rotor efficiency coefficient, , is 0.47.

A Introduction to Wind Power

61

Exercise 3 Power Versus Wind Speed Review Questions

4. Describe how the torque developed at the rotor of a wind turbine varies as afunction of the rotor speed. Explain what is meant by the maximum powerpoint (MPP), and why the wind turbine must be operated as close as possibleto the optimum speed.

5. Refer to the mechanical power-versus-speed curves and electrical powerversus-speed curves of Figure 28 and Figure 29. How does the mechanicalpower at the maximum power point (MPP) vary with rotor speed? Why?Does the maximum electrical power produced by the wind turbine generatorvary in the same way as the MPP with rotor speed?